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A network optimization tool

Copyright 2001 A.V. Hill Associates

10316 Meade Lane

Eden Prairie, MN 55347 USA

ahill@csom.umn.edu

952-942-56790

Netsolver is a network optimization tool that can quickly find the optimal solution to a

wide variety of problems. All you have to do is to define the network of arcs on the"arcs" worksheet, and then go to the "optimize" worksheet and click "start." Netsolver

quickly finds the minimum cost flow through the network that satisfies all of the arc

constraints -- and then re orts the results on the o timization worksheet.

A network is defined in terms of nodes and arcs. Arcs are defined in terms of a

beginning node label, an ending node label, a minimum flow, a maximum flow, and a

cost per unit flow. Node labels can be of any length, are not case sensitive, and can

include special characters (including internal blanks). You must have one node labeled

as the "source" node and another as the "sink" node. The algorithm will follow the

conservation of flow rule which states that the flow going into an arc must equal the flow

going out of an arc. You can have more than one arc between any two nodes -- butNetsolver will alwa s ut flow throu h the chea er arc first.

Netsolver uses "short" integers for the minimum flow, maximum flow, cost/unit flow, and

the flow variables. So be careful that you don't have a cost or flow that is greater than

the largest "short" integer, which is 32,767. It is okay, however, for the total cost for an

arc or for the solution to be greater than this value. Do not use any decimals anywhere

in Netsolver.

This code is an implementation of the Ford and Fulkerson out-of-kilter algorithm. This

is not the fastest algorithm available -- but is still quite fast and meets the needs of mostusers. The student version of the code is limited to 20 nodes and 100 arcs.

Netsolver is an implementation of the Ford and Fulkerson out-of-kilter algorithm. This is

not the fastest algorithm available -- but is still quite fast and meets the needs of most

users. The student version is limited to 20 nodes and 100 arcs. The premium edition

with over 1,000 nodes and 10,000 arcs is available from the author.

mailto:ahill@csom.umn.edumailto:ahill@csom.umn.edu

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Netsolver is a powerful way to handle a variety of important single-commodity standard

problems such as (1) the assignment problem, (2) the transportation problem, and (3)

the transshipment problem. Multiple period problems can be handled easily by

"shipping" product from one period into the next (with the appropriate carrying cost).

The model can be applied to shipping problems, shortest path problems, dynamicdemand lotsizin roblems, and man others.

Revised 4/7/01

Disc lamer: The author m akes no guarantees that th is works correct ly !

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Arcs

From To

n mum

flow

ax mum

flow

ost un t

flow

Source A1 1 1 0

Source B1 1 1 0Source C1 1 1 0

Source D1 1 1 0

Source E1 1 1 0

A1 B2 0 1 2

A1 C2 0 1 2

A1 D2 0 1 5

A1 E2 0 1 6

B1 A2 0 1 2

B1 C2 0 1 4

B1 D2 0 1 3

B1 E2 0 1 4

C1 A2 0 1 2C1 B2 0 1 4

C1 D2 0 1 7

C1 E2 0 1 6

D1 A2 0 1 5

D1 B2 0 1 3

D1 C2 0 1 7

D1 E2 0 1 1

E1 A2 0 1 6

E1 B2 0 1 4

E1 C2 0 1 6

E1 D2 0 1 1

A2 Sink 1 1 0

B2 Sink 1 1 0

C2 Sink 1 1 0

D2 Sink 1 1 0

E2 Sink 1 1 0

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Optimize

Click to start or stop the optimization

Summary of the resultsNetsolver student edition program limits:

Number of nodes 12 Maximum number of nodes 20

Number of arcs 31 Maximum number of arcs 100

Final status Feasible

Elapsed time (seconds) 0.2

Total cost 10

Number of iterations 813

Arc results( If a feasible solut ion is fo und, on ly arcs with Cost x Flow greater than zero are shown .)

From node To node Minimum Maximum Cost/unit Flow Cost x Flow

A1 B2 0 1 2 1 2

B1 C2 0 1 4 1 4

C1 A2 0 1 2 1 2

D1 E2 0 1 1 1 1

E1 D2 0 1 1 1 1

Start Stop